Simplify; express your answer in exponential form. Assume $a\neq 0, r\neq 0$. $\dfrac{{a}}{{(a^{-2}r^{-2})^{-3}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${a}$ to the exponent ${1}$ . Now ${1 \times 1 = 1}$ , so ${a = a}$ In the denominator, we can use the distributive property of exponents. ${(a^{-2}r^{-2})^{-3} = (a^{-2})^{-3}(r^{-2})^{-3}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{a}}{{(a^{-2}r^{-2})^{-3}}} = \dfrac{{a}}{{a^{6}r^{6}}}$ Break up the equation by variable and simplify. $\dfrac{{a}}{{a^{6}r^{6}}} = \dfrac{{a}}{{a^{6}}} \cdot \dfrac{{1}}{{r^{6}}} = a^{{1} - {6}} \cdot r^{- {6}} = a^{-5}r^{-6}$.